Gender-neutral mermaid
I found this reference on reddit:
Singular of folk would just be "person."
Merfolk would be a community of merpeople, or a merperson if singular.
The word "merrow" has been used as a (possibly) gender-neutral for similar creatures. It is not actually as closely related to "mermaid" and "merman" as it might appear (although it is ultimately related). It comes from an Irish word, so it is mainly used in Irish English and to refer to mermaids and mermen in the context of Irish folklore. Also, it seems mermen are rare in Irish folklore, and the term "merrow" is only viewed as including males by some people: others view it as an exclusively feminine designation (for example, this website about "Irish Fairies").
The Oxford English Dictionary defines the word merrow as "a mermaid or a merman," and says it comes from Irish "muruach, murúch < Early Irish murdúchann siren < muir sea (see mere n.1) + dúchann song". The root of muir is the same as German Meer, Latin mare and the archaic English mere. Wikipedia says that there was some uncertainty in the past about the derivation of the second half of the word. The usual pronunciation is given as /ˈmɛroʊ/, although this seems to be derived from the spelling (the OED says that the English Dialactal Dictionary recorded the pronunciation as /ˈmərə/).
Wikipedia also says that "The merrow which signifies 'sea maiden' is an awkward term when applied to the male, but has been in use" which isn't exactly a glowing endorsement of this usage, but I think anyone would agree that it at least doesn't sound as awkward as "mermaid" in reference to a male.
I'm not sure I would recommend using "merrow" as a gender-neutral singular, but I think it's at least good to be aware of the word when considering your options.